Question

On a hot summer day, a student turns his fan on when he leaves his room in the morning. When he returns in the evening, will the room be warmer or cooler than the neighboring rooms? Why? Assume all the doors and windows are kept closed.

Short answer

Answer: The student's room will be warmer than the neighboring rooms. This is due to the fan generating additional heat from converting electrical energy into thermal energy, and the lack of air exchange between the room and the neighboring rooms.

Step-by-step solution

Understanding Fan Operation

A fan works by circulating the air inside a room. When the fan is turned on, its blades spin rapidly, creating air currents. These air currents move hot air away from the body and replace it with cooler air from the surrounding room, providing a cooling effect to the person in the room. However, the fan does not actually reduce the temperature of the air in the room; it just makes it feel cooler by distributing the air evenly.

Heat Transfer and Energy Conversion

When a fan is in operation, it converts electrical energy into kinetic energy, which is the movement of the fan blades. Some of this energy is also converted into thermal energy due to the friction between the moving parts of the fan and the surrounding air. This additional thermal energy increases the heat content of the room.

Comparing Temperatures

Since the fan is generating additional heat within the room, the overall temperature of the room will gradually increase, even if the air circulation makes it subjectively feel cooler. If we compare the room with the fan turned on with the neighboring rooms, the room with the fan will be warmer due to the heat generated by the fan.

Room with Closed Doors and Windows

In this exercise, we assume that all the doors and windows are kept closed, meaning that there is little to no exchange of air between the room with the fan and the neighboring rooms. This further supports the conclusion that the room with the fan will be warmer, as the generated heat cannot escape to the neighboring rooms.

Conclusion

Based on the analysis above, we can conclude that when the student returns to his room in the evening after leaving his fan on throughout the day, the room will be warmer than the neighboring rooms. This is due to the fan generating additional heat from the conversion of electrical energy into thermal energy, and the lack of air exchange between the room and the neighboring rooms.